Speaker
Dr
Elena Vedmedenko
(University of Hamburg)
Description
The correlation function is an essential ingredient of any
theory of phase transitions, covering electronic systems,
liquids or magnets, since it provides direct information on
critical properties of a system. With the Ornstein-Zernike
law its general analytical form is known for infinite
systems at infinite observation times, above the critical
temperature.
However, important experimental developments involve
ever smaller length- and time-scales connected with
size- and time-dependent phases like thermally assisted
switching of magnetization. For such nano-sized
systems, there is up to now no clear understanding of
crossover phenomena like the crossover from a
paramagnetic state at high temperatures via a
superparamagnetic regime to ferro- or antiferromagnetic
order at low T, and how they manifest themselves in the
correlation function. This is related to the problem that a
Curie (or Neel) temperature cannot be defined
unambiguously. These problems hamper a reliable
interpretation of experimental results.
In this talk I will present a particularly simple general
expression for the correlation function, covering all
sample sizes L, all observation times, and the entire
temperature range from zero to infinity. Our numerical
and analytical calculations demonstrate that the Curie
temperature does not simply decrease with decreasing
sample size but rather splits in finite samples for finite
observation times. This new result obtained for open
boundaries does not violate scaling invariance and
recovers all known laws for periodic boundary
conditions, infinite observation times and high
temperatures as limiting cases. The proposed form for
the correlation function allows for a novel and effective
procedure to determine above mentioned splitting and
critical temperatures which goes beyond the famous
Binder cumulants method as it permits an accurate
determination of the Curie temperature of infinite and
finite objects, as well as the blocking temperature, from
a single calculation of a finite object without tedious
finite-size scaling.
Primary author
Dr
Elena Vedmedenko
(University of Hamburg)
